Method and apparatus for fabrication of large area 3D photonic crystals with embedded waveguides

ABSTRACT

In accordance with some aspects of the present disclosure, a maskless interferometric lithography system for fabricating a three-dimensional (3D) photonic crystal using a multiple two-beam-exposures is disclosed. The system can comprise an illumination system comprising an optical arrangement operable to receive radiation from a radiation source and provide three or more tilted two-beam interference pattern exposures to be combined into a three-dimensional pattern; and a substrate operable to be supported by a substrate table, wherein the substrate comprises a photoresist formed on a top surface of the substrate and operable to receive the three-dimensional pattern and wherein means are provided to adjust the position of the substrate in all six mechanical degrees of freedom.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.14/844,470 filed on Sep. 3, 2015, which is a divisional of U.S. patentapplication Ser. No. 13/365,964 filed on Feb. 3, 2012, now U.S. Pat. No.9,152,040 issued Oct. 6, 2015, which claims priority to U.S. ProvisionalPatent Application No. 61/439,722 filed on Feb. 4, 2011, both of whichare hereby incorporated in their entireties by reference.

GOVERNMENT INTEREST

This invention was made with U. S. Government support under Contract No.FA9550-09-100202 awarded by the Air Force Office of Scientific Research.As a result the U. S. Government has certain rights in this invention.

FIELD OF THE INVENTION

This invention relates generally to photonic crystals and, moreparticularly, to materials and methods of large area three-dimensional(3D) photonic crystals and to waveguides embedded within the 3D photoniccrystals.

BACKGROUND OF THE INVENTION

A three-dimensional (3D) crystal has a periodic dielectric function inall three orthogonal Cartesian directions (x, y, z-axes). 3D photoniccrystals are attractive for very compact waveguide devices. There arenumerous ways to fabricate 3D photonic crystals (PhCs) includingion-beam milling, multi-step lithography and etching (woodpileapproach), and 4 or 5-beam holography. The ion-milling and woodpileapproaches are process intensive and have alignment or inter-levelregistration issues. Single-exposure, multi-beam holography has theadvantage of being able to form PhCs in a single lithography step, buthas limitations on the PhC shape and size, including interrelationshipsbetween the various periodicities that restrict the available parameterspace.

Interferometric lithography (IL) is a well established technique forproducing 2D, e. g. confined to a photoresist layer on a substrate withvariations in the plane of the substrate but not perpendicular to thesubstrate plane, gratings down to a λ/4n half-pitch where λ is theexposure wavelength and n the refractive index of any immersion medium(n=1 for air). IL has a large depth-of-focus with inherent uniformityfor forming large-area gratings on photoresist-coated wafers. Using IL,there is no need to use a mask or lens system to produce small pitchstructures. This creates an inexpensive, large-area fabricationcapability for sub-micrometer pitch periodic features.

An issue in conventional multi-beam (typically 4 or 5 beams) approachesto 3D IL is that the z-pitch is constrained by the physics of theoptical configuration and is typically much larger than the (x-, y-)pitches, for cases where the exposure wavelength is much shorter thanthe PhC pitch. This is the usual case where the exposure wavelength isin the ultraviolet region of the spectrum while the PhC is designed forvisible or infrared wavelengths. Note that throughout this disclosurethe pitches will be referred to as the orthogonal (x-, y- and z-)directions notwithstanding the fact that different symmetry photoniccrystals have different unit cells which may not align with theseCartesian directions.

Additionally, in conventional single exposure IL, the pitch in all threedirections is a function of each of the plane-wave beam angles and theexposure wavelength. In order to obtain a photonic crystal (PhC) withthe x, y, and z pitches similar to each other, the exposure beam angle θmust be as close as possible to 90°, and the exposure wavelength must beclose to the desired pattern pitch dimension. For example, if thedesired PhC pitch is 750 nm then the exposure wavelength needs to be^(˜)750 nm. This is difficult because it requires a photoresist that issensitive at that wavelength, and if the desired pitch is changed thenthe photoresist and the laser source also need to be changed. Mostavailable photoresists are designed for ultraviolet and deep-ultravioletlight, rather than for infrared light. Some applications, for example totelecommunications systems, require periodicities corresponding toinfrared wavelengths, where commercial photoresists are typically notavailable.

Photonic crystals have many useful properties and more applications areavailable by combining PhCs with integrated optical waveguides.Waveguides in PhCs can guide light around sharp bends, filter light,spit or mix light into multiple waveguides, and provide opticalisolators and optically coupled cavities. As a result of the confinementover long path lengths, as compared with bulk material propagation,waveguides embedded in a PhC can also exhibit non-linear opticalproperties that can be used for optical computing applications. Mosttechniques for embedding waveguides into PhC involve either forming thedefects or waveguide when fabricating the PhC in a layer-by-layerfashion, or by a direct write, two-photon method used for typicalholographically produced PhCs. In all cases the embedded waveguideformation is a tedious and slow process.

Chiral, coil-spring-like helical photonic crystal structures, are usefulfor optical applications including: circular polarizers, optical diodes,and optical isolators. A chiral material lacks any planes of mirrorsymmetry, and is characterized by a cross coupling between the electricand the magnetic material response. This results in breaking thedegeneracy between the two circularly polarized waves; i.e., therefractive index is increased for one circular polarization and reducedfor the other. This gives rise to interesting phenomena that are notavailable from conventional materials including the possibility of anegative refractive index for one circular polarization while therefractive index for the other circular polarization remains positive.

Traditionally helical structures have been formed using either glancingangle deposition (GLAD), a technique based on physical vapor depositionthat employs oblique angle deposition conditions, or serial direct laserwriting based on multi-photon absorption. Both of these techniques areslow and unsuitable for fabricating helical structures over large areas.

SUMMARY

In accordance with aspects of the present disclosure, a masklessinterferometric lithography system for fabricating a three-dimensional(3D) photonic crystal using multiple, two-beam exposures is disclosed.The system can comprise an illumination system including an opticalarrangement operable to receive radiation from a radiation source,characterized by both a longitudinal and a transverse coherence andprovide two beams at the substrate with overlapping regions of the twobeams within the longitudinal and transverse coherence lengths whereinthe angle between the wave vectors of each beam and the normal to thesubstrate surface can be independently adjusted over two subsets of therange from −90° to +90°; and a substrate operable to be supported by asubstrate table, wherein the substrate comprises a photoresist formed ona top surface of the substrate and operable to receive thethree-dimensional pattern. The degrees of adjustment of the substratetable can include all six rigid body degrees of freedom. Additionallayers, such as an antireflection layer may be interspersed between thesubstrate and the photoresist; additionally, the substrate itself mayconsist of a layered material structure.

In some aspects, the system can further comprise one or more actuatorsoperable to move the substrate, the substrate table, or both thesubstrate and the substrate table in one or more degrees of freedom withrespect to the illumination system. In some aspects, the one or moredegrees of freedom can comprise rotation of the substrate, the substratetable, or both the substrate and the substrate table in a directionazimuthal to an optical axis of the illumination system. In someaspects, the one or more degrees of freedom can comprise a rotationabout the z-axis (normal to the substrate), tilts about both x- andy-axes, or both a rotation and two tilts of the substrate table.

In some aspects, the illumination and substrate systems can be operableto provide a multiplicity of two-beam exposures, each two-beam exposureconsisting of the intensity interference between two approximately planewave coherent optical beams incident at two angles from the normal tothe substrate wherein the tilt of the interference planes in thephotoresist corresponds to the average of the two incident angles in thephotoresist. Each of these two-beam exposures is further characterizedby an azimuthal angle which is varied between exposures. In variousinstantiations, the multiplicity is either three, four, or six and theazimuthal angles are either 120°, 90°, or 60° from each other. Inaddition to controlling the angles of incidence and azimuth, in someinstantiations the phase of the interference pattern relative toprevious exposures, or to a reference grid on the substrate, is alsocontrolled within the illumination and substrate systems.

In some aspects, the system can further comprise an immersion systemarranged to provide an immersion fluid to a portion of the substratetable, the substrate, or both the substrate table and the substrate. Insome aspects, the immersion fluid can be provided by an inlet of theimmersion system to at least optically homogeneously fill the spacebetween the last optical element of the optical system and the top ofthe photoresist layer over the area to be exposed atop the substrateduring at least one of the exposures by the optical system. In someaspects, the immersion system can comprise a flow control system tocontrol the flow of the immersion fluid provided by the inlet.

The interference pattern in the photoresist has the highest visibility,defined as the difference between intensity maxima and minima divided bythe sum of the intensity maxima and minima,[(I_(max)−I_(min))/(I_(max)+I_(min))], when the electric fieldamplitudes of the two beams in the photoresist are equal, and all partsof the overlapping beams are positioned within the longitudinal andtransverse coherence lengths of the source. The highest visibility inthe exposure pattern results in the highest contrast latent imagefringes following the exposure and the most well-defined structures ondeveloping the photoresist. Accordingly, in some aspects various opticalelements are introduced in the system to control the beams to arrangethese conditions.

In some aspects, the system can further comprise one or more opticalcompensators operable to control and/or compensate for path lengthdifferences of the two-beams in the illumination system, to within thelongitudinal and transverse coherence lengths of the laser source. Insome aspects, the one or more optical compensators can comprise one ormore actuators coupled to one or more optical elements of theillumination system operable to adjust a path length of one or moreradiation beams directed onto the one or more optical elements. This isto arrange the beams so that they are within a longitudinal coherencelength of the source.

In some aspects, the system can further comprise one or more astigmatictelescopic systems in one or both legs of the illumination systeminterferometer to adjust the beam sizes at the substrate plane such thatthe interfering regions of the two beams are within the transversecoherence length of the source.

In some aspects, the system can further include an optical system toadjust intensity ratios of the radiation such that each transmittedbeams of radiation into the photoresist have substantially commonelectric field amplitudes and therefore a visibility approaching unity.

In some aspects, this optical system can comprise a Fresnel reflectionwindow operable to continuously adjust relative powers of the twocoherent radiation beams by rotating the window relative to apropagation direction of the radiation to adjust a ratio of reflectedand transmitted power through the Fresnel reflection widow.

In some aspects, control systems can be provided operable to adjust theoptical systems included to control the path lengths of the arms of theexposure system, the transverse sizes and relative alignments of thearms of the interferometer beams at the substrate, and the intensitiesof the arms of the interferometer beams in the photoresist to optimizethe visibility of the fringe pattern in the photoresist.

In some aspects, the system can comprise a control system coupled to theone or more actuators and operable to monitor an interference patternproduced by the optical system and by an auxiliary interferometricmonitor system to provide one or more signals to the one or moreactuators to optimize the relationships between the multipleinterference patterns projected onto the substrate by directing the oneor more actuators to move the substrate table in one or more degrees offreedom.

In some aspects, the average of the incident angles in at least one ofthe two-beam exposure provided by the illumination system can bearranged to be off-axis relative to the substrate normal.

In some aspects, the 3D PhC can have hexagonal symmetry.

In some aspects, the 3D PhC can have rectangular symmetry.

In some aspects, the 3D PhC can have helical [chiral] symmetry.

In some aspects, the 3D PhC can have trigonal symmetry.

In some aspects, the 3D PhC can have orthorhombic symmetry.

In some aspects, the 3D PhC can have monoclinic symmetry.

In some aspects, the system can further comprise an alignment systemoperable to align the substrate, the substrate table, or both thesubstrate and the substrate table with one or more alignment orregistration marks in one or more degrees of freedom.

In some aspects, the system can further comprise a substrate holderoperable to secure the substrate onto the substrate table.

In some aspects of the present disclosure, a method of fabricating athree-dimensional (3D) photonic crystal comprising using amultiple-exposure, two-beam interferometric lithography (IL) arrangementis disclosed. The multiple-exposure method can comprise tilting, withthe centerline between the two beams tilted relative to the surfacenormal, and azimuthally rotating the various exposures from each other.The method can comprise generating a shortened z-pitch than thatavailable from a single multi-beam exposure. The method can furthercomprise incorporating immersion fluids in the interferometriclithography arrangement to further increase the available range of (x-,y-, z-) pitches.

In some aspects of the present disclosure, a method of fabricating awaveguide integrated with a photonic crystal (PhC) comprising using afirst wavelength exposure to define a waveguide in a photoresist layerand using a second wavelength exposure to define a PhC in thephotoresist, and a photoresist development step to instantiate both thewaveguide and the PhC is disclosed. In some aspects, the secondwavelength exposure to define a PhC comprises a series of two-beam ILexposures.

In some aspects of the present disclosure, a method of fabricating awaveguide integrated with a photonic crystal (PhC) is disclosed. Themethod can comprise providing a first photoresist layer on a substrate;defining a waveguide region by exposing a surface of the firstphotoresist layer using a first wavelength, wherein an absorption depthand exposure dose of the first wavelength is used to set the thicknessof the waveguide; forming a second photoresist layer on the firstphotoresist layer containing the defined waveguide; and defining aphotonic crystal throughout the bulk of the photoresist by exposing thetwo layers of photoresist at a second wavelength, wherein thephotoresist is substantially transparent at the second wavelength.Further, this aspect includes development of the photoresist after allof the exposures have been completed.

In some aspects, the PhC can be formed using traditional lithographystepper or scanner using multiple exposures with a phase shift mask andoff-axis illumination.

In some aspects of the present disclosure, a method of modifying thedeveloped photoresist structures to enhance the contrast between therefractive indices of the two materials by using sol-gel infiltration,pyrolysis, deposition and plating of metals and dielectrics isdisclosed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example multiple-exposure IL approach in accordance withaspects of the present disclosure.

FIG. 2 shows an example multiple-exposure IL approach in accordance withaspects of the present disclosure.

FIG. 3 shows exemplary steps for a three-exposure 3D hexagonal IL PhC.

FIG. 4 shows an example illumination system comprising a Michelsoninterferometer that can be used to provide the interfering beams for thetwo-beam exposures in accordance with aspects of the present disclosure.

FIG. 5 shows another example illumination system comprising a Michelsoninterferometer in accordance with aspects of the present disclosure.

FIG. 6 shows another example illumination system comprising a Michelsoninterferometer in accordance with aspects of the present disclosure.

FIG. 7 shows another example illumination system comprising a Michelsoninterferometer in accordance with aspects of the present disclosure.

FIG. 8 shows another example illumination system comprising a Michelsoninterferometer with an alignment system in accordance with aspects ofthe present disclosure.

FIG. 9 shows another example illumination system comprising a Michelsoninterferometer in an immersion environment in accordance with aspects ofthe present disclosure.

FIG. 10 shows example plot of available z-pitches versus available x (y)pitches for an exposure wavelength of λ=355 nm, photoresist index ofrefraction n_(r)=1.3, and an immersion medium index of 1.0.

FIG. 11 shows an example plot of available z-pitches versus available x(y) pitches for an exposure wavelength of λ=355 nm, a photoresist indexof refraction n_(r)=1.7, and an immersion medium index of 1.0.

FIG. 12 shows example plot of available z-pitches versus available x (y)pitches for an exposure wavelength of λ=355 nm, a photoresist index ofrefraction n_(r)=1.7, and an immersion medium index of 1.4.

FIG. 13 shows example plot of available z-pitches versus available x (y)pitches for an exposure wavelength of λ=248 nm, a photoresist index ofrefraction n_(r)=1.3, and an immersion medium index of 1.0.

FIG. 14 shows example plot of available z-pitches versus available x (y)pitches for an exposure wavelength of λ=193 nm, a photoresist index ofrefraction n_(r)=1.7, and an immersion medium index of 1.4.

FIG. 15 shows a mathematical model for an exemplary 3D hexagonal IL PhCmade using 3 exposures with 120° rotation in accordance with thedisclosed multiple-exposure IL technique.

FIG. 16 shows results from experiments for exemplary cubic 3D IL PhCformed using 3 exposures with 120° rotation in accordance with variousembodiments of the present teachings.

FIG. 17 shows results from a mathematical model for exemplary cubic 3DIL PhCs made using 4 exposures with 90° rotation in accordance withvarious embodiments of the present teachings.

FIG. 18 shows results from experiments for exemplary cubic 3D IL PhCsmade using 4 exposures with 90° rotation in accordance with variousembodiments of the present teachings.

FIG. 19 shows exemplary steps for a six-exposure 3D helical IL PhC.

FIG. 20 shows cross-section of a 3D helical pattern and pitchdefinitions.

FIG. 21 shows a mathematical model for exemplary helical PhC made using6 exposures with 60° rotations in accordance with various embodiments ofthe present teachings.

FIG. 22 shows results from experiments for exemplary helical PhCaccording various embodiments of the present teachings.

FIG. 23 shows various fabrication processes of waveguides embeddedwithin photonic crystals in accordance with various embodiments of thepresent teachings.

FIG. 24 shows results from experiments for a single layer 355 nmthree-exposure 3D PhCs with a 244 nm surface waveguides exposure innegative photoresist.

FIG. 25 depicts results from experiments for a dual layer 355 nmthree-exposure 3D PhC with an embedded 244 nm waveguide exposure innegative photoresist that after fabrication was subjected to a chemicaletch-back process in order to reveal the individual layers of the PhCand the embedded waveguide.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to the exemplary embodiments of theinvention, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers will be usedthroughout the drawings to refer to the same or like parts. In thefollowing description, reference is made to the accompanying drawingsthat form a part thereof, and in which is shown by way of illustrationspecific exemplary embodiments in which the invention may be practiced.These embodiments are described in sufficient detail to enable thoseskilled in the art to practice the invention and it is to be understoodthat other embodiments may be utilized and that changes may be madewithout departing from the scope of the invention. The followingdescription is, therefore, merely exemplary.

The 3D photonic crystals can be formed by a multiple exposure two-beaminterferometric lithography technique, which allows for independentdimensional control of the period along each axis of the crystal. Forexample, each individual crystal lattice constant can be adjusted over awide range (within the optics constraint that each lattice constant islarger than λ/2n_(r) where λ is the source wavelength and n_(r) therefractive index of the photoresist), greatly increasing the availableparameter space and allowing the use of UV lasers and photoresistsleveraging off of conventional lithographic capabilities for PhCs scaledto visible and near-infrared wavelengths. The disclosed lithographyprocess can be performed with significantly relaxed constraints on thesize, shape and periodicities and having independent control over eachperiodic pitch of the formed 3D PhCs. Specifically, a two-beaminterferometric lithography setup and multiple exposures followed by asingle development step can be used to form 3D PhCs. In contrast,prior-art multiple-beam single-exposure interferometric lithographytechniques using 3, 4, 5 or more beams have inherent constraints betweenthe lattice constants and the exposure wavelength.

Further, in an interferometric lithographic system there is no maskdefining the pattern, but rather a radiation beam is split into twobeams, and the two beams are caused to interfere at a target portion ofsubstrate through the use of a reflection system. The interferencecauses lines to be formed on at the target portion of the substrate. Forpositive tone resists the lines correspond to the intensity minima ofthe interferometric standing wave pattern; for negative tone resists thelines correspond to the intensity maxima of the interferometric standingwave pattern.

The term “illumination system” used herein should be broadly interpretedas encompassing any type of illumination system, including refractive,reflective, magnetic, electromagnetic and electrostatic optical systems,or any combination thereof, as appropriate for the exposure radiationbeing used, or for other factors such as the use of an immersion liquidor the use of a vacuum.

Various embodiments provide materials and methods of fabricatingthree-dimensional (3D) photonic crystals (PhCs) with or withoutwaveguides embedded in the 3D photonic crystals. Various embodimentsalso include photonic crystals with integrated waveguides. Thewaveguides can be embedded inside the 3D photonic crystals by usingmultiple exposure wavelengths, with one set of exposures at a wavelengththat propagates throughout the photoresist for the PhC fabrication and asecond at a wavelength that may be highly absorbed in the photoresistfor the waveguide fabrication. Such processes can be scalable tomanufacturing using standard semiconductor lithography equipment.

A mathematical model of the 3D PhCs and/or the waveguides formed withinthe PhCs can also be used to facilitate the formation of the exemplary3D PhCs, to compare with or measure the experimentally produced PhCs.

In the 3D exposure model of the exemplary 3D multiple, two-beam exposureIL, the intensity for all exposures is normalized to 1/N for simulationswhere N is the number of two beam exposures. This assumes that eachexposure has the same exposure dose. This convention is adopted forconvenience and is not a necessary restriction; for some applicationsunequal intensities may be of advantage. Using a simple threshold modelfor the photoresist development, the expected 3D structures can becalculated. This model is a simplification of the actual photoresistdevelopment; nonetheless it provides a good approximation and is verycomputationally efficient allowing rapid investigation of a large numberof exposure sequences and parameters. More accurate photoresist exposureand development models are known in the art and can be used for refinedstructure prediction and evaluation.

An exemplary advantage of the disclosed multiple, two-beaminterferometric lithography exposure approach can include a much greaterflexibility to independently control the periodicities of the resulting3D structures along each axis as compared with prior-art multiple-beamsingle-exposure approaches. The x-pitch and y-pitch of the pattern inthe exposure plane can be controlled by the angle between the twoexposure beams 2θ_(Δ). The z-pitch of the pattern, perpendicular to theexposure plane, can be controlled by the angle of the intercept betweenthe two beams to the normal of the exposure plane ψ, see FIG. 6. Inembodiments, the z-pitch can be obtained similar to or the same as thex- and y-pitch.

If both exposure beams are tilted off normal to the exposure plane (ψ≠0)the interference pattern in the photoresist is also tilted. As a resultthe different indices of refraction of the incident medium and thephotoresist, the incident plane waves of light are bent at thephotoresist interface, see FIG. 6. For a vertical interference pattern(ψ=0) θ₁=−θ₂, if both θ₁ & θ₂ are offset by a fixed angle there can be ashift in the interference pattern angle ψ_(c). The following formulasgive the relations between the plane-wave beam angles in the air and inthe photoresist as well as some of the defined pitches (periods), referfor FIGS. 1 and 2. Angles to the left side of normal have positivevalues, and angles to the right side of normal have negative values.

$\theta_{1.{PR}} = {a{\sin\left\lbrack \frac{\sin\left( \theta_{1} \right)}{n_{r}} \right\rbrack}}$$\theta_{2.{PR}} = {a{\sin\left\lbrack \frac{\sin\left( \theta_{2} \right)}{n_{r}} \right\rbrack}}$$\psi = \frac{\theta_{1} + \theta_{2}}{2}$$\theta_{\Delta} = {{\frac{\theta_{2} - \theta_{1}}{2}\psi_{c}} = {{\frac{\theta_{1.{PR}} + \theta_{2.{PR}}}{2}\theta_{\Delta.{PR}}} = \frac{\theta_{2.{PR}} - \theta_{1.{PR}}}{2}}}$$\Lambda_{X} = {\Lambda_{X.{air}} = {\Lambda_{X.{PR}} = {\frac{\lambda}{{\sin\;\left( \theta_{2} \right)} - {\sin\left( \theta_{1} \right)}} = \frac{\lambda}{n_{r} \cdot \left\lbrack {{\sin\left( \theta_{2.{PR}} \right)} - {\sin\left( \theta_{1.{PR}} \right)}} \right\rbrack}}}}$$\Lambda_{c} = {{\Lambda_{X} \cdot {\cos\left( \psi_{c} \right)}} = \frac{\lambda}{2 \cdot n_{r} \cdot {\sin\left( \theta_{\Delta.{PR}} \right)}}}$$\Lambda_{Z} = \frac{\Lambda_{X}}{\tan\left( \psi_{c} \right)}$

If three or more of these tilted interference pattern exposures arecombined a three-dimensional pattern that has a shortened z-pitch,compared with that available for a single, multiple-beam exposure, canbe generated. FIGS. 1 and 2 show slice views of a possible 3D PhCstructure. As shown, if ψ_(c)=45°, then Λ_(x)=Λ_(z). This can be used toform symmetrical 3D PhCs.

FIG. 3 shows exemplary steps for a three exposure, two-beam IL 3D PhC.As shown, the first exposure results in a latent image, e.g. a patternof chemical bond modifications that will result in variations in thelocal dissolution rate of the resist in a developer after appropriatesteps including post-exposure baking, of a one-dimensional grating withtilted lines in the photoresist coating on a substrate. In embodiments,additional thin-film layers such as anti-reflection layers, as known inthe art, can be incorporated either above or below the photoresistlayer. After 120° rotation of the photoresist-coated sample, the secondexposure produces a second latent image tilted at the same angle to thesurface normal but rotated 120° azimuthally from the lines of the firstlatent image. After an additional and final 120° rotation of the samplethe third and final exposure can sum with the first two exposures tofrom a latent image of 3D PhC in the photoresist. The photoresist canthen be baked and developed to form the 3D PhC. During the formationprocess, the rotation and tilt of the wafer between exposures can becontrolled.

In embodiments if the rotation or tilt is not set precisely as discussedabove, a phase variation along the crystal planes will be generated.This is not present in a single two-beam IL exposure, but rather resultsfrom the overlay between all three or more patterns. This will cause amoiré effect on the PhC, that is, the phase of the PhC will varyperiodically across the wafer. A laser interferometer or other devicewith similar function can be used to monitor and provide feedbackcontrol of tilt, rotation, and phase between exposures.

FIG. 4 shows an example illumination system comprising aninterferometer, such as a Michelson interferometer, that can be used toprovide the interfering beams for the two-beam exposures. The Michelsoninterferometer can use beamsplitter 405, such as a 50/50 beam splitter,to split an input beam 400, such as an UV beam, from one radiationsource (not shown) and directed by optical element 410 and opticalelement 415, such as a mirror 1 and mirror 2, into two beams 420 and425, which can have equal intensity. The split two beams can include,e.g., reflected beam 420 and transmitted beam 425. Transmitted beam 425can be directed to a photoresist (not shown) provided on a top surfaceof a sample (not shown) via optical element 435, such as mirror 4, at anangle of about θ_(Δ) from a normal of the sample. The sample can bearranged on a substrate (wafer) 440, which can be supported by asubstrate table (stage) 445. Reflected beam 420 can be directed to thephotoresist to be combined with the transmitted beam 425 via opticalelement 450, such as mirror 3, and optical element 455, such as mirror5, at an angle of about θ_(Δ) from the normal of the sample. The opticalelements of the illumination system can be arranged with respectivemounts (not shown) that can be actuated. Controller 460 can be operableto actuate substrate table 445 in one or more degrees of freedom. Forexample, controller 460 can be operable to rotate the stage or wafer indirection about an axis perpendicular or substantially perpendicular toa top surface of the wafer or stage. By way of another example,controller 460 can be operable to tilt the stage or wafer in one or moredegrees of freedom. The beams in FIG. 4 are arranged symmetrically aboutthe normal to the substrate. As a consequence, the interference fringesin the photoresist are normal to the substrate as in the inset to FIG.1.

FIG. 5 shows another example illumination system comprising aninterferometer, such as a Michelson interferometer, that can be used toprovide the interfering beams for the two-beam exposures. The Michelsoninterferometer can use beamsplitter 515, such as a 50/50 beam splitter,to split an input beam 505, such as an UV beam, from one radiationsources (not shown) and directed by optical element 510, such as amirror 1, into two beams 520 and 525, which can have equal intensity.The split two beams can include, e.g., reflected beam 525 andtransmitted beam 520. Transmitted beam 520 can be directed to wafer 555by optical element 530, such as mirror 2 and optical element 540, suchas mirror 3. Reflected beam 525 can be directed onto wafer 555 supportedon exposure stage (substrate table) 560 by optical element 550, such asmirror 4, and combined with radiation reflected from optical element540. The optical elements of the illumination system can be arrangedwith respective mounts that can be actuated by a controller to effect achange in the path length of the radiation. Controller 565 can beconnected to or coupled to stage 560 to adjust the stage 560 or wafer555 in one or more degrees of freedom. For example, controller 565 canbe operable to rotate the stage or wafer in direction about an axisperpendicular or substantially perpendicular to a top surface of thewafer or stage. By way of another example, controller 565 can beoperable to tilt the stage or wafer in one or more degrees of freedom.In FIG. 5, both beams of the interferometer are tilted to the same sideof the substrate normal, giving rise to tilted fringes in thephotoresist layer as in FIG. 1.

FIG. 6 shows another example illumination system comprising aninterferometer, such as a Michelson interferometer, that can be used toprovide the interfering beams for the two-beam exposures. The Michelsoninterferometer can use beamsplitter 615, such as a 50/50 beam splitter,to split an input beam 605, such as an UV beam, from one radiationsources (not shown) and directed by optical element 610, such as amirror 1, into two beams 620 and 625, which can have equal intensity.The split two beams can include, e.g., reflected beam 625 andtransmitted beam 620. Transmitted beam 620 can be directed to wafer 665by optical element 630, such as mirror 2, and optical element 640, suchas mirror 3. Reflected beam 625 can be directed onto wafer 655 supportedon exposure stage (substrate table) 660 by a telescope arrangement,including optical element 670, such as lens 1, and optical element 675,such as lens 2, and optical element 650, such as mirror 4, and combinedwith radiation reflected from optical element 640. The optical elementsof the illumination system can be arranged with respective mounts thatcan be actuated by a controller to effect a change in the path length ofthe radiation. Controller 665 can be connected to or coupled to stage660 to adjust the stage 660 or wafer 655 in one or more degrees offreedom. For example, controller 665 can be operable to rotate the stageor wafer in direction about an axis perpendicular or substantiallyperpendicular to a top surface of the wafer or stage. By way of anotherexample, controller 665 can be operable to tilt the stage or wafer inone or more degrees of freedom. The function of the telescope, lenses670 and 675, is to allow overlap of the two beams to within thetransverse coherence length of the source. Since the impact of the tiltis only in the plane of the figure, these are preferably cylindricallenses.

FIG. 7 shows another example illumination system comprising aninterferometer, such as a Michelson interferometer, that can be used toprovide the interfering beams for the two-beam exposures. The Michelsoninterferometer can use beamsplitter 715, such as a 50/50 beam splitter,to split an input beam 705, such as an UV beam, from one radiationsources (not shown) and directed by optical element 710, such as amirror 1, into two beams 720 and 725, which can have equal intensity.The split two beams can include, e.g., reflected beam 725 andtransmitted beam 720. Transmitted beam 720 can be directed to fusedsilica window 735 via optical element 730, such a mirror 2, where aportion of transmitted beam 720 is directed to beam block 745 and theremaining portion is directed to wafer 755 by optical element 740, suchas mirror 3. Reflected beam 725 can be directed onto wafer 755 supportedon exposure stage (substrate table) 760 by optical element 750, such asmirror 4, and combined with radiation reflected from optical element740. The optical elements of the illumination system can be arrangedwith respective mounts that can be actuated by a controller to effect achange in the path length of the radiation. Controller 765 can beconnected to or coupled to stage 760 to adjust the stage 760 or wafer755 in one or more degrees of freedom. For example, controller 765 canbe operable to rotate the stage or wafer in direction about an axisperpendicular or substantially perpendicular to a top surface of thewafer or stage. By way of another example, controller 765 can beoperable to tilt the stage or wafer in one or more degrees of freedom.

Fused silica window 735 is operable as a variable attenuator to ensurethat the intensities of beams incident on the photoresist of wafer 755are substantially similar since it is important to have high contrast inthe fringes of the interferometric exposures. Window 735 is operable tobe rotated with an actuator (not shown) to change its reflectivity,which allows for matching the intensities of the beams incident on wafer755. In some aspects, a variable attenuator can be used instead ofwindow 735. Alternatively, a half wave plate that is operable to rotatethe polarization of the incident radiation and a polarizer that isarranged to only transmit the polarization that is matched with theother beam can be used instead of window 735. Beam block 745 is operableto absorb the power reflected from window 735 to at least limit theamount of radiation that an operator of the illumination system mayexperience and to reduce the occurrence of stray light or flareinadvertently impinging on the photoresist layer. In some aspects, beamblock 745 is not required for operation of the illumination system.

FIG. 8 shows another example illumination system comprising a Michelsoninterferometer with an alignment system in accordance with aspects ofthe present disclosure. FIG. 8 is similar to the arrangement shown inFIG. 7, with the addition of the alignment system, which can also beused in the arrangement shown in FIGS. 4-7 and 9, discussed below. Thealignment system can be arranged in the form of a second Michelsoninterferometer and can include a secondary radiation source 805, such asa HeNe laser, beam splitter 810, mirror 815, converging lens 820, phasesensitive detection (PSD) system 825, and controller 830. The opticalelements of the alignment system can be arranged in respective mountscan that be actuated by controller 830 to change the optical path of theradiation beam.

FIG. 9 shows another example illumination system comprising a Michelsoninterferometer in an immersion environment in accordance with aspects ofthe present disclosure. FIG. 9 is similar to the arrangement shown inFIG. 7, with the addition of an immersion system. The immersion systemcan be used with the illumination system to increase the range offeature sizes which can be produced in the photoresist and specificallyto permit the production of smaller features that correspond topropagation of the beams at steeper angles in the photoresist. Theimmersion system can be arranged in a variety of manners, as would beapparent. For example, an immersion fluid 905, such as water, can beprovided to at least a portion of the wafer 755 by one or more fluidinlets coupled to the substrate table. The immersion fluid can becontained within a localized area below the final optical element of theillumination system and can be confined within that location by aconfinement system, such a one or more barrier members including a gasbarrier. The immersion fluid can be removed by one or more fluid outletscoupled to the substrate table. An optical element 910, such as a prismcan be positioned near the portion of the wafer being imaged to receiveradiation being directed toward the wafer and to allow for introductionof the interfering beams into the photoresist at steeper angles than areavailable without the immersion system.

In the examples illumination systems discussed above with respect toFIGS. 4-9, the intensities of the two beams can be different for anumber of reasons including: 1) the beamsplitter 405, 515, 615, and 715could have a splitting ratio that depends on the manufacture of thebeamsplitter and might need some adjustment; 2) there are differentoptics in the two beam paths after the beamsplitter that might havedifferent cumulative transmissions; 3) the beams are incident on thephotoresist at different angles, so there are different Fresnelreflectivities from the photoresist surface; and 4) the beam sizes couldbe different because of the different angles of incidence, which couldresult in different intensities for the same power in each beam.

The optical elements, for example mirrors 1-4 can be arrangedappropriately for the needed exposure angles and path lengths for bothsplit beams provided by the beamsplitter. For example, beam splitter405, 515, 615, and 715 and optical element 435, 540, 640, and 740 can bepositioned left or right such that the path length of beam 1 is equal tothe path length of beam 2. Having the same path length for both beamscan maximize the interference pattern contrast and allow the maximumexposure area consistent with the laser coherence length. Inembodiments, the input beam can be split in a manner that the twoexposure beams can overlay each other with the same orientation, inother words, can match portions of the beams that split at the beamsplitter and interfere with themselves at the exposure plane. In somecases, this can be essential for making large exposure areas if thelight source, such as an excimer laser, has a small transversecoherence.

The optical configuration of FIGS. 4, 5, and 7 is appropriate for asource with a transverse coherence greater than the beam size, as in thecase, for example, for a single transverse mode laser source. For theopposite case of a source with a transverse coherence much less than thebeam size, as is the case, for example, for an excimer laser, it isnecessary to provide additional, astigmatic telescopic optics to adjustthe beam sizes of at least one arm of the illumination interferometer sothat the interfering portions of the two beams are within the transversecoherence length of the source, as shown in FIG. 6.

In the example optical configurations of FIGS. 4-9, a sample can bearranged on a substrate (wafer) 440, 555, 655, and 755 and supported bysubstrate table (stage) 445, 560, 660, and 760. The sample can include aphotoresist provided on a top surface of the sample that is responsiveto the radiation provided by the illumination system.

In some aspects, the beamsplitters 405, 515, 615, and 715 of FIGS. 4-9can be a phase-mask beamsplitter, phase-grating beamsplitter, and/or aplate beamsplitter. As would be apparent to those of ordinary skill inthe art, the optical requirements of 1D and 2D interferometriclithography, when using a phase-mask beamsplitter, may need to beadjusted as needed.

To better understand the relation and parameter space for the z-pitch(period) compared to the transverse (e.g., lateral or x,y) pitches(periods), FIGS. 10-14 shows example plots of available z-pitches versusavailable x (y) pitches for various conditions, including variousexposure wavelengths and indexes of refraction for the photoresist(n_(r)). FIG. 10 shows a plot for an exposure wavelength of λ=355 nm andphotoresist index of refraction n_(r)=1.3, where the line 1005represents the z-pitch versus x(y)-pitch for on-axis 3D IL PhCs, or inother words, represents the locus for the z-period versus thex(y)-period for on-axis single-exposure multi-beam 3D IL PhCs. Area 1010represents the combinations of z-pitches and x-pitches achievable withoff-axis multiple two-beam 3D IL PhCs, or in other words, represents themuch greater range of combinations of z-periods versus x-periodsachievable with off-axis multiple, two-beam exposure 3D IL PhCs. Thedashed line 1015 represents the symmetrical PhC (z-pitch=x-pitch).

FIG. 11 shows an example plot of available z-pitches versus available(x-, y-) pitches for an exposure wavelength of λ=355 nm, a photoresistindex of refraction n_(r)=1.7, more characteristic of currentlyavailable commercial resists, and an immersion medium refractive index,n_(m)=1.0 (e.g. air). The space of available pitches is smaller as aresult of the bending of the interferometric beams on entering thehigher index photoresist. FIG. 12 shows example plot of availablez-pitches versus available (x-, y-) pitches for an exposure wavelengthof λ=355 nm, a photoresist index of refraction n_(r)=1.7, and animmersion medium index of n_(m)=1.4. The higher index of the immersionmedium, for example water, allows recovery of the larger space ofavailable pitches as in FIG. 10. FIG. 13 shows example plot of availablez-pitches versus available (x-, y-) pitches for an exposure wavelengthof λ=248 nm, a photoresist index of refraction n_(r)=1.3, and animmersion medium refractive index of n_(m)=1.0. FIG. 14 shows exampleplot of available z-pitches versus available (x-, y-) pitches for anexposure wavelength of λ=193 nm, a photoresist index of refractionn_(r)=1.7, and an immersion medium index of n_(m)=1.4. As a result ofthe shorter wavelength, smaller features are possible in thisconfiguration.

FIG. 15 depicts mathematical models for an exemplary 3D PhC made usingthe disclosed multiple, two-beam exposure IL technique. The first set ofimages focuses on the PhCs made using a three-exposure process (with120° rotations of the sample) that creates 3D PhC with hexagonalsymmetry.

FIG. 16 depicts SEM images of exemplary 3D PhCs made using the disclosedmultiple, two-beam exposure IL technique. This set of images shows PhCsmade using a three-exposure process (with 120° rotations of the sample)that creates a 3D PhC with hexagonal symmetry. The experimental PhCs aremade in Futurrex NR7-6000P negative photoresist at a thickness of 12 μmexposed at 355 nm using a frequency tripled Nd:YAG laser with a largetransverse coherence length. These conditions apply to all of theexamples presented herein.

In FIG. 16, the exemplary silicon wafer substrate is cleaved forcross-sectioning and the formed PhC on the surface is also cleaved alongits crystal planes. As seen from the SEM images in FIG. 16, the PhC isuniform over the 10-μm² imaged area, while the overall size of theformed PhC is about 2 cm² by 12 μm thick. In embodiments, smallvariations from the surface to the bottom of the photonic crystal can beobserved, which are significantly distinguished from the variation ofthe nodes due to the photonic crystal cleave angle. For example,variation in the photonic crystal hole size is likely due to variationin exposure dose versus photoresist depth from light absorption in thephotoresist, and to a smaller extent from developer diffusion andconcentration variations during the development process.

As observed, across the PhC area there can be phase shifts along thesurface for every ^(˜)3-5 mm, which appear as faint fringes on the PhCto the naked eye. These phase shifts can be from variations of theexposure plane due to wafer flatness or tilt. The void sizes in thecrystal structure vary slightly from edge to edge of the 2-cm² PhCmostly due to exposure variations. For the top-down SEM images in FIG.16, three periods down into the crystal are visible. The top down SEMclearly shows the hexagonal symmetry.

FIGS. 17 and 18 depict exemplary cubic 3D IL PhCs made using 4 exposureswith 90° rotation in accordance with various embodiments of the presentteachings. Specifically, FIG. 17 depicts results from the mathematicalmodel, and FIG. 18 depicts results from experiments. The four-exposure3D PhC fabrication of a rectangular structure shown in FIGS. 17 and 18can be similar to the three-exposure process depicted in FIGS. 15 and16. However, the additional exposure requires additional rotational andwafer tilt alignments.

In FIG. 18, the exemplary silicon wafer substrate is cleaved forcross-sectioning and the formed PhC on the surface is also cleaved alongits crystal planes, which are slightly out of alignment with the siliconcleavage plane. The formed PhC can be uniform over the 10-μm² areaimaged with an overall size of about 2 cm² by 12 μm. For the top-downSEM images in FIG. 18, four periods down into the crystal are visible.As mentioned above, the variation in the photonic crystal pore size islikely due to variation in exposure dose versus photoresist depth fromlight absorption in the photoresist, and to a smaller extent fromdeveloper diffusion and concentration fluctuations during developing.Also, across the PhC area there are phase shifts along the surface forevery ^(˜)2-3 mm, and the void sizes in the crystal structure varyslightly from edge to edge. The top down SEM clearly shows an exemplarysquare symmetry.

Three-dimensional helical photonic crystals are attractive for chiralmetamaterial devices that mix electrical and magnetic responses. Inchiral metamaterials, the refractive index for propagation of lightalong the axis of the helix is different as the handedness of thecircular polarization is parallel or antiparallel to the chiral axis.The refractive index is increased for one circular polarization andreduced for the other, if the chirality is strong enough, negativerefraction may occur. In some aspects, a multiple exposure two-beaminterferometric lithography (IL) technique utilizing six separatetwo-beam exposures for fabricating 3D helical photonic crystals may beused. In contrast to most previous demonstrations which used atwo-photon direct-write process, IL is a large-area process readilyadaptable to realistic manufacturing constraints. This novelinterferometric lithography uses only TE polarized light for maximumcontrast and allows for independent dimensional control of the helixpitch and periodicity along each lattice axis. Both mathematical modelsand experimentally realized three-dimensional helical photonic crystals(over an mm² in area and up to 5 μm tall, with a helix spacing of 890 nmon a hexagonal grid) are presented. The helical photonic crystals can beformed as a thick photoresist structure that can be subsequently used asa mandrel for a sol-gel or metal electroforming process, enabling a highindex contrast chiral metamaterial.

In some aspects of the present disclosure, an exemplary technique isdisclosed that can create dense arrays of helical structures (3D PhC)using a simple, parallel, large-area lithography process with thecapability to regulate the size, shape and periodicities of the crystal,allowing independent control over the helical lattice periodicity andcoil pitch of the 3D PhC. This technique consists of a simple two-beamoff-axis Michelson interferometric lithography arrangement with multipleexposures followed by a single development step.

The helical pillar photoresist structures are prone to collapse duringthe drying step of the development process due to the surface tensionapplied to the high aspect ratio and small substrate contact area of thephotoresist. The inverse structures, helical holes, can be obtained bylowering the exposure dose, and will not have any issues with patterncollapse. These inverse helical pillars can subsequently be used as amandrel for a sol-gel or metal electroforming process, enabling a highindex contrast chiral metamaterial. This initial demonstrationconcentrated on the helical pillars.

FIG. 19 shows the steps in the definition of a six-exposure 3D IL PhCthat provides the helical structures. The first exposure results in alatent image of a one-dimensional grating with tilted lines in thephotoresist. After a 60° rotation about the sample normal and a π/3phase-shift in the z-direction the second exposure sums with the firstto form a latent image of a 2D array of tilted posts in the photoresist.After additional 60° rotations, π/3 phase-shifts, and exposures of thesample, all of the exposures sum in the photoresist (each exposure iscoherent; they sum incoherently) to form a latent image of a 3D helicalPhC. The summed latent image after each exposure is shown in FIG. 19,depicting how each exposure is added together to achieve the finalhelical structure. The photoresist is then post-exposure baked anddeveloped to result in the final 3D helical PhC. The phase-shift,rotation and tilt of the exposure stage between exposures needs to betightly controlled in three-dimensional IL. The π/3 phase-shift in thez-plane between exposures is necessary to achieve the desired spiralingof the latent image to form the helical PhC. If the rotation or tilt isnot set precisely, an undesirable phase variation will result along theexposure plane (essentially a moiré pattern). This will cause a phaseshift of the helical pillars across the PhC. In the experiments, a HeNelaser interferometer was used to monitor and provide feedback control ofthe phase shift, tilt and rotation between exposures.

Both images created by mathematical models and by SEM images of theexperimental 3D PhCs using the multiple-exposure IL setup are presented.The set of images were made using a six-exposure process (with 60°rotations and π/3 phase-shift in the z-plane between each exposure) thatcreates a 3D helical PhC. The experimental PhCs are made in FuturrexNR7-6000P negative photoresist at a thickness of 5 μm exposed at 355 nm.

FIG. 21 shows close-up simulations of the helical PhC made by the6-exposure off-axis interferometry lithography. The simulation modelparameters were: ψ=45°, θ_(Δ)=8°, ϕ=60°, N=6, n_(r)=1.7, λ=355 nm, andThreshold=62%. The (x-,y-) pitch of these structures is 1.8 μm and thez-pitch is 4 μm. In FIG. 22, experimental SEM images are shown. Thesilicon wafer substrates of the experimental PhCs are cleaved forcross-section SEMs. The PhC is very uniform over the 10-μm² area imaged;the overall size of the PhC was ^(˜)2 cm² by 5 μm. Any variation in thephotonic crystal coil size is likely due to variations in exposure doseversus photoresist depth resulting from light absorption in thephotoresist, and to a smaller extent from developer diffusion andconcentration fluctuations. The coil sizes in the crystal structure varyslightly from edge to edge of the 2-cm² PhC mostly due to exposurevariations. For the top-down SEM images in FIG. 22, one full rotation ofthe crystal coils is visible. The top down SEM clearly shows thehexagonal symmetry of the helical crystals.

FIGS. 19-21 depict exemplary model results for helical (chiral) 3D ILPhCs made using 6 exposures with 60° rotation between two-beam exposuresin accordance with various embodiments of the present teachings. FIG. 22depicts results from experiments. The six-exposure 3D PhC fabrication ofa helical structure shown in FIG. 19 can be similar to thethree-exposure process depicted in FIGS. 15 and 17. However, additionalexposure requires additional rotational and wafer tilt alignments. Theoptical properties of these helical symmetry structures have potentialapplication in polarization manipulation and in negative-indexmaterials. It is also necessary in these exposures to control therelative phases (absolute positions of the light and dark fringes at afixed plane, e.g. the top surface of the photoresist). For eachexposure, corresponding to a 60° azimuthal rotation, the phase is alsoadjusted by π/3. This was not necessary in the three exposure case,unless a specific phase of the PhC was desired; in this case the 0° and180° exposures (and the other equivalent pairs—60° and 240°; 120° and300°) are required to have this phase relationship.

In FIG. 22, the exemplary silicon wafer substrate is cleaved forcross-sectioning. The formed PhC can be uniform over at least the 10-μm²area imaged with an overall size of about 2 cm² by 12 μm thick. For thetop-down SEM images in FIG. 22, four periods down into the crystal arevisible. Across the PhC area there are phase shifts along the surfacefor every ^(˜)2-3 mm, and the helical size of the crystal structurevaries slightly from edge to edge. The top down SEM clearly shows anexemplary hexagonal symmetry of the helical structures.

Waveguides can be fabricated, embedded within PhCs by using twodifferent exposure wavelengths in separate exposures of the photoresistfilm. For example, the first wavelength can be used to create the latentimage of the PhC as disclosed herein, and the second wavelength can beused to create the latent image of the waveguides within the PhCs. Bothexposures can be in the same layer of photoresist material, which isdisposed on a substrate. The exposures are then followed with a commonpost-exposure bake and development process

In one embodiment, the waveguide is exposed, by standard lithographytechniques, in a first photoresist layer using a wavelength that isstrongly absorbed by the photoresist. After development, this exposurewill result in a waveguide region confined to the near surface region ofthe photoresist and extending into the resist by approximately anabsorption length at the exposing wavelength. In some aspects, a buriedwaveguide can be formed that can be, fully surrounded by the PhC byusing a second layer of photoresist that can be spun on to the firstlayer of photoresist and post-application baked. These two layers ofthick photoresist become the body of the PhC. Now the two layers ofphotoresist are exposed using the multiple, two-beam IL exposuretechnique at a wavelength for which the photoresist is very transparentto form the PhC. Following the exposures, the photoresist ispost-exposure baked. Then the full two-layer photoresist stack isdeveloped. The resulting photoresist pattern can be the functional sumof the two different wavelength exposures forming a PhC with embeddedwaveguides. The lateral size of the waveguide defect is a directfunction of the waveguide mask pattern size and the waveguide exposuredose, and the thickness of the waveguide is a direct function of thephotoresist absorption length at the waveguide exposure wavelength plusthe waveguide exposure dose. For a surface waveguide, the second layerof photoresist is not used.

FIG. 23 depicts various fabrication processes of waveguides embeddedwithin photonic crystals in accordance with various embodiments of thepresent teachings. As shown, waveguides can be formed in any positionwithin the later formed PhCs. For example, waveguides can be formed inthe center of the two-layer-photoresist (or the formed PhCs), and/or beformed on the surface of the two-layer-photoresist (or the formed PhCs).

As disclosed herein, the photoresist can be selected to respond toexposure at both wavelengths for forming the waveguide and for formingthe PhC. For example, many photoresists used in the semiconductorindustry are sensitive to light over a large range of wavelengths. Inone embodiment, a negative I-line photoresist used to make a PhC can besensitive to a 244-nm light that is used to make the waveguide.Similarly a positive 248-nm photoresist used to make a PhC can besensitive to a 193-nm-light that can be used to make the waveguide. Insome embodiments, the photoresist can have the same tone for bothwavelengths. In other embodiments, having the same photoresist tone atboth wavelengths is not a requirement. For example, a photoresistusually acts as either a positive material or negative material at bothwavelengths, but the process steps can be modified to produce similarresults if the photoresist has a positive tone response at onewavelength and a negative tone at the other wavelength.

For PhC exposure, the selected photoresist can be transparent and have ahighly nonlinear (thresholding) response curve at the PhC wavelength. Asknown, most photoresists are substantially transparent at their designwavelengths and exhibit a nonlinear response to the incident intensityduring the exposure and development processes. For the waveguideexposure, the transparency of the photoresist at the exposing wavelengthcan play an important role. For example, if the photoresist istransparent at the waveguide exposure wavelength then the waveguide canextend through the full thickness of the photoresist. This can bedesirable for two-dimensional PhCs, wherein the same wavelength can beused for both exposures. However if the photoresist is highly absorptiveat the waveguide exposure wavelength, then the waveguide will exist onthe surface of the crystal as shown in FIG. 23. By tailoring theabsorption of the photoresist at the waveguide exposure wavelength, thewaveguide thickness can be controlled.

In embodiments, the described techniques can be expanded to more thantwo layers of the photoresist. For example, a three-layer process can beused to fabricate a layer of embedded waveguides patterns that are ⅓from the bottom of the PhC and a second layer of embedded waveguidespatterns that are ⅔ from the bottom of the PhC. Using processingvariations, vertical waveguides between the two embedded waveguidelayers can be fabricated using a via exposure patterning step on thesecond photoresist layer. This via pattern exposure can be performedeither by using a high dose at the waveguide exposure wavelength, orusing a third exposure wavelength with lower photoresist absorption thanthe waveguide exposure wavelength. In this case, optical circuits can beintegrated and fabricated into the PhC.

In an exemplary embodiment, 3D PhCs with waveguides can be fabricated innegative tone photoresist, using a three- and a four-exposure ILprocess. FIG. 24 depicts SEM results for a single layer 355 nmthree-exposure 3D PhCs with a 244 nm surface waveguides exposure inFuturrex NR7-6000P negative photoresist. Waveguides formed on thesurface of the PhCs can be seen more easily in the SEM than waveguideformed in the center of the PhC. FIG. 25 depicts SEM results for a duallayer 355 nm three-exposure 3D PhC with an embedded 244 nm waveguideexposure in Futurrex NR7-600P negative photoresist that afterfabrication was subjected to a chemical etch-back process in order toreveal the individual layers of the PhC and the embedded waveguide. Inmost cases, the embedded waveguides appear as a missing void in thecleaved section of the PhC in cross-section SEM images. These are notvisible in the top-down SEM images.

In this manner, a 3D PhC can be fabricated based on multiple-exposure,two-beam IL with off axis illumination. The disclosed IL techniques canbe used to produce PhCs over large areas, as indicated by both modeledand experimental photoresist profiles of 3D PhCs. In embodiments, 3DPhCs can be made of high quality over large two square centimeter areasby IL. In addition to the large 3D photonic crystals, waveguides can beintegrated into the PhCs in the fabrication process and in the finalstructures using the disclosed multiple-wavelength lithographytechnique, wherein a first wavelength is used to create the PhC using ILand a second wavelength is used to create the waveguide using standardlithography. As disclosed herein, waveguides integrated with 3D PhCs canprovide other devices including but not limited to narrow-band filters;waveguide bends, splitters, and resonators; channel-drop filters; andcoupled-cavity waveguides.

One limitation of the present experimental crystals can be that the PhCslack a full photonic band-gap as a result of the low index contrastbetween the photoresist and air. A larger index contrast is required forthe PhCs to exhibit a full band-gap. This can be achieved by using thephotoresist PhC as scaffolding for a higher index material. One suchmethod is an inverse-opal technique where a liquid sol-gel is introducedinto the voids of the PhC and solidified during a curing step. A secondmethod is to fill the voids of the PhC with a metal using anelectroforming process in a plating bath. Both of these cases can createan inverse of the original PhC. The subsequent photoresist scaffoldingcan then be removed using O₂ plasma or some other chemical processes.Additionally, preprocessing can be done before the infiltration step;one example is pyrolysis to oxidize the photoresist, leaving anamorphous carbon film with dramatically reduced dimensions of theinterconnects, but the same x,y dimensions of the nodes as a result ofthe adhesion to the substrate.

Optical properties of PhCs also can be controlled by modifying thedeveloped photoresist structure. Such modification can include, e.g.,incorporation of nanoparticles onto the surface of the photoresiststructure, chemically altering the photoresist compound through the useof chemically reactive gases or liquids, and/or a post process thatmodifies the optical properties of the photoresist compound.

Another limitation can be that the demonstrated PhCs do not have fullsymmetry in the x, y, and z directions. In the present exemplary cases,full crystal symmetry is not achieved because the z-dimension is notscaled down sufficiently as a result of the high index of thephotoresist (e.g., n^(˜)1.7) and the resulting Snell's law limitationson angle of propagation from the normal as the incident beams enter thephotoresist. To further scale 3D PhCs using the multiple-exposuretwo-beam IL to smaller sizes and thus shorter band-gap wavelengths, theangles of the beams can be made larger. The larger the angle between thetwo beams the smaller the pitch of the crystal in the x and ydirections. Likewise the larger the angle of the intercept of the twobeams from normal of the exposure plane, the smaller the pitch in the zdirection, although there is a limit associated with the Fresnel bendingof the input beams at the air/photoresist interface. However, this canbe addressed by using one or more of: immersion techniques (to reducethe Fresnel effects by lowering the index contrast on entering theresist); shorter actinic wavelengths; or lower index photoresists.

In embodiments, the fabrication process for the two-wavelength approachcan include disposing an anti-reflective coating (ARC) between thephotoresist and the substrate. This ARC is used to minimize thereflection of the exposure light off of the substrate. The ARC caneither be a dielectric layer or a spun-on organic layer. Then a thickphotoresist layer can be formed, e.g., spun atop the ARC. Thephotoresist is then baked to drive out solvents and to crosslink thephotoresist.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the invention are approximations, the numericalvalues set forth in the specific examples are reported as precisely aspossible. Any numerical value, however, inherently contains certainerrors necessarily resulting from the standard deviation found in theirrespective testing measurements. Moreover, all ranges disclosed hereinare to be understood to encompass any and all sub-ranges subsumedtherein. For example, a range of “less than 10” can include any and allsub-ranges between (and including) the minimum value of zero and themaximum value of 10, that is, any and all sub-ranges having a minimumvalue of equal to or greater than zero and a maximum value of equal toor less than 10, e.g., 1 to 5. In certain cases, the numerical values asstated for the parameter can take on negative values. In this case, theexample value of range stated as “less than 10” can assume negativevalues, e.g. −1, −2, −3, −10, −20, −30, etc.

Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope and spiritof the invention being indicated by the following claims.

What is claimed is:
 1. A method of fabricating an embedded waveguideintegrated with a photonic crystal (PhC) comprising: providing a firstphotoresist layer on a substrate; proving first optical irradiation toform a latent image of a waveguide by exposing a surface of the firstphotoresist layer using a first wavelength, wherein an absorption depthand an exposure dose of the first wavelength is used to set a thicknessof the waveguide; forming a second photoresist layer on the firstphotoresist layer containing the previously exposed latent image of thewaveguide; providing second optical irradiation to form a latent imageof a photonic crystal throughout a bulk of the first photoresist layerand the second photoresist layer by exposing both the first photoresistlayer and the second photoresist layer at a second wavelength, whereinthe first photoresist layer and the second photoresist layer aresubstantially transparent at the second wavelength; developing both thefirst photoresist layer and the second photoresist layer to create thewaveguide and the photonic crystal after exposures have been made; andmodifying photoresist structures that are developed to enhance arefractive index contrast by using sol-gel infiltration, pyrolysis,deposition and plating of metals and dielectrics.
 2. The method inaccordance with claim 1, further comprising providing three or morelayers of photoresist and providing two or more independent waveguideexposures respectfully.
 3. The method of claim 1, further comprisingproviding, by an immersion system, an optically homogeneous immersionfluid to an exposure region between a final optical element of anillumination system and both the first photoresist layer and the secondphotoresist layer along with an optical system to expand a range ofaccessible tilt angles of radiation in both the first photoresist layerand the second photoresist layer beyond those available without theimmersion fluid.
 4. The method of claim 1, wherein the second opticalirradiation comprises multiple two-beam interferometric exposureswherein the substrate is moved in one or more degrees of freedom withrespect to an illumination system between each two-beam interferometricexposure.
 5. The method of claim 4, further comprising measuring andcontrolling a position of the substrate with respect to the illuminationsystem in six rigid body degrees of freedom by a measurement andactuation system.
 6. The method of claim 4, wherein the one or moredegrees of freedom comprises rotation of a substrate normal, a tiltabout two in-plane coordinates, or both rotation and tilts of asubstrate table.
 7. A method of fabricating an embedded waveguideintegrated with a photonic crystal (PhC) comprising: providing firstirradiation to form a latent image of a waveguide by exposing a surfaceof a first photoresist layer on a substrate using a first wavelength,wherein an absorption depth and an exposure dose of the first wavelengthis used to set a thickness of the waveguide; forming a secondphotoresist layer on the first photoresist layer containing thepreviously exposed latent image of the waveguide; providing, by animmersion system, an optically homogeneous immersion fluid to anexposure region between a final optical element of an illuminationsystem and the first photoresist layer and a second photoresist layeralong with an optical system to expand a range of accessible tilt anglesin the first photoresist layer and the second photoresist layer beyondthose available without the immersion fluid; providing secondirradiation to form a latent image of a photonic crystal throughout abulk of the first photoresist layer and the second photoresist layer byexposing both the first photoresist layer and the second photoresistlayer at a second wavelength, wherein the first photoresist layer andthe second photoresist layer are substantially transparent at the secondwavelength; developing both the first photoresist layer and the secondphotoresist layer to create the waveguide and the photonic crystal afterexposures have been made; and modifying photoresist structures that aredeveloped to enhance a refractive index contrast by using sol-gelinfiltration, pyrolysis, deposition and plating of metals anddielectrics.
 8. The method of claim 7, further comprising providingthree or more layers of photoresist and providing two or moreindependent waveguide exposures respectively.
 9. The method of claim 7,wherein the second optical radiation comprises multiple two-beaminterferometric exposures wherein the substrate is moved in one or moredegrees of freedom with respect to an illumination system between eachtwo-beam interferometric exposure.
 10. The method of claim 9, whereinthe one or more degrees of freedom comprises rotation of a substratenormal, a tilt about two in-plane coordinates, or both rotation andtilts of a substrate table.
 11. The method of claim 7, furthercomprising measuring and controlling a position of the substrate in sixrigid body degrees of freedom by a measurement and actuation system. 12.A method of fabricating an embedded waveguide integrated with a photoniccrystal (PhC) comprising: providing first optical UV radiation to form alatent image of a waveguide by exposing a surface of a first photoresistlayer on a substrate using a first wavelength, wherein an absorptiondepth and an exposure dose of the first wavelength is used to set athickness of the waveguide; forming a second photoresist layer on thefirst photoresist layer containing the previously exposed waveguide;providing second optical UV radiation to form a latent image of aphotonic crystal throughout a bulk of the first photoresist layer andthe second photoresist layer by exposing the two layers of photoresistat a second wavelength, wherein the first photoresist layer and thesecond photoresist layer are substantially transparent at the secondwavelength; developing both the first photoresist layer and the secondphotoresist layer to create the waveguide and the photonic crystal afterthe exposures have been made; and modifying photoresist structures thatare developed to enhance a refractive index contrast by using sol-gelinfiltration, pyrolysis, deposition and plating of metals anddielectrics.
 13. The method of claim 12, further comprising providingthree or more layers of photoresist and providing two or moreindependent waveguide exposures respectfully.
 14. The method of claim12, wherein the second optical UV radiation comprises multiple two-beaminterferometric exposures wherein the substrate is moved in one or moredegrees of freedom with respect to an illumination system between eachtwo-beam interferometric exposure.
 15. The method of claim 12, furthercomprising measuring and controlling a position of the substrate in sixrigid body degrees of freedom by a measurement and actuation system. 16.The method of claim 12, further comprising moving the substrate in oneor more degrees of freedom with respect to an illumination system usingone or more actuators, wherein the one or more degrees of freedomcomprises rotation of a substrate normal, a tilt about two in-planecoordinates, or both rotation and tilts of a substrate table.
 17. Themethod of claim 12, further comprising providing, by an immersionsystem, an optically homogeneous immersion fluid to an exposure regionbetween a final optical element of the illumination system and the firstphotoresist layer along with an optical system to expand the range ofaccessible tilt angles in both the first photoresist layer and thesecond photoresist layer beyond those available without the immersionfluid.